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Experimental verification of the quantum nature of a neural network

Andrei T. Patrascu

TL;DR

The paper investigates whether quasi-classical neural networks can harbor genuine quantum properties due to the dynamics of their maps. It develops a framework that blends category-theoretic and gauge-theoretic ideas with Hamilton–Jacobi dynamics to show how entanglement can emerge from learning rules, independent of quantum constituents. A practical route is proposed to extract inner entanglement via a neural network coupled to external quantum systems, described by a density-matrix formalism and analyzed with an entanglement witness such as concurrence $C( ho)$. The work suggests that quantum resources could be realized in noisy, macroscopic settings and points toward potential experimental tests with physically implemented neural networks, with implications for quantum-inspired computation and quantum biology.

Abstract

Neural networks are being used to improve the probing of the state spaces of many particle systems as approximations to wavefunctions and in order to avoid the recurring sign problem of quantum monte-carlo. One may ask whether the usual classical neural networks have some actual hidden quantum properties that make them such suitable tools for a highly coupled quantum problem. I discuss here what makes a system quantum and to what extent we can interpret a neural network as having quantum remnants. I suggest that a system can be quantum both due to its fundamental quantum constituents and due to the rules of its functioning, therefore, we can obtain entanglement both due to the quantum constituents' nature and due to the functioning rules, or, in category theory terms, both due to the quantum nature of the objects of a category and of the maps. From a practical point of view, I suggest a possible experiment that could extract entanglement from the quantum functioning rules (maps) of an otherwise classical (from the point of view of the constituents) neural network.

Experimental verification of the quantum nature of a neural network

TL;DR

The paper investigates whether quasi-classical neural networks can harbor genuine quantum properties due to the dynamics of their maps. It develops a framework that blends category-theoretic and gauge-theoretic ideas with Hamilton–Jacobi dynamics to show how entanglement can emerge from learning rules, independent of quantum constituents. A practical route is proposed to extract inner entanglement via a neural network coupled to external quantum systems, described by a density-matrix formalism and analyzed with an entanglement witness such as concurrence . The work suggests that quantum resources could be realized in noisy, macroscopic settings and points toward potential experimental tests with physically implemented neural networks, with implications for quantum-inspired computation and quantum biology.

Abstract

Neural networks are being used to improve the probing of the state spaces of many particle systems as approximations to wavefunctions and in order to avoid the recurring sign problem of quantum monte-carlo. One may ask whether the usual classical neural networks have some actual hidden quantum properties that make them such suitable tools for a highly coupled quantum problem. I discuss here what makes a system quantum and to what extent we can interpret a neural network as having quantum remnants. I suggest that a system can be quantum both due to its fundamental quantum constituents and due to the rules of its functioning, therefore, we can obtain entanglement both due to the quantum constituents' nature and due to the functioning rules, or, in category theory terms, both due to the quantum nature of the objects of a category and of the maps. From a practical point of view, I suggest a possible experiment that could extract entanglement from the quantum functioning rules (maps) of an otherwise classical (from the point of view of the constituents) neural network.
Paper Structure (10 sections, 135 equations, 3 figures)

This paper contains 10 sections, 135 equations, 3 figures.

Table of Contents

  1. Introduction
  2. a brief categorical interpretation
  3. how is a classical neural network quantum?
  4. where are the wavefunctions?
  5. non-separability of a neural network
  6. extracting the inner entanglement of a neural network, a practical approach
  7. conclusion
  8. Data Availability Statement
  9. Competing interests
  10. Funding

Figures (3)

  • Figure 1: The evolution of information in a simple neural network. The red wavefront shows the direction in which information is separable. The gradient back-propagation however, drawn as the blue wavefront makes the global information on the network non-separable and the overall state space of the network more "quantum"
  • Figure 2: The averaged interaction potential for a two layers network as evolving in time. The negative values for time are due to the conventional choice of the initial moment of input
  • Figure 3: The evolution of concurrence over a series of time iterations of the density matrix